NUMERICAL ANALYSIS (SAYISAL ÇÖZÜMLEME) 2015 WEEK 2

SOLVE BY COMPUTER PROGRAM :

EX1 Re-write the program NA5(Newton Raphson method) to find root of  f(x)=x³-3 function. Note that you should also define the derivative

EX2 Re-write Newton-Raphson.xls to find roots of f(x)=x³-3 function by Newton-Raphson method.

EX3 Re-write the program NA6 and NA7 (Secant  method) to find root of  f(x)=x³-3 function.

EX4 Re-write secant_1.xls,  secant_2.xls, and secant_3.xls,    to find roots of f(x)=x³-3 function by secant methods.

EX5 Solve root of function f(x)=13*(x - x*x)*exp(-3*x/2) by using

a) Inverse lagrange interpolation method

b) Newton-bisection combined method

c) Brent method

EX7 : In round smooth tubes for turbulent flow region Fanning friction factor is given as:

This equation is valid for 4 * 10³ < Re < 3 * 10⁶   By using one of the root finding methods, calculate friction factor for Re=5000. You can utilize any root finding method you learned so far.

EX10: Determine the real root of f(x)=-12-21x+18x²-2.75x³ by using

 a) Newton-Raphson Method

 b) Secant method

 c) Muller method

SOLVE BY HAND

EX11 :  Find all real roots of function

EX12 Find root of f(x)=x³-2x²-3, starting form x=1 by Newton-Raphson method by hand calculations

EX13 Find root of f(x)=x³-2x²-3, starting form x=1 by Secant method by hand calculation
sEX14 Find root of f(x)=x³-2x²-3, starting form x=1 by Inverse lagrange interpolation method by hand calculations